Borehole imagery is a major component of the wireline business (for example, Schlumberger's FMI™, Formation MicroScanner, OBMI™ Tools), and an increasing part of the logging while drilling business (Schlumberger's GeoVision™) (as described by Tilke, “Imagery in the Exploration for Oil and Gas”, published in Castelli et al., Image Databases (2002) Wiley, page 608, incorporated by reference herein in its entirety). While these measurements contain abundant data about the subsurface, it remains a challenge to automatically extract the important geological and petrophysical knowledge contained therein. The precise and efficient extraction of this knowledge from the images increases their utility, and therefore will increase the demand for these measurements.
Schlumberger has a long interest in developing techniques for automatically interpreting and extracting features from borehole imagery. Many of the most successful techniques in this area have been implemented in Schlumberger's BorTex™, PoroSpect™ and BorDip™ applications. BorTex™ semi-automatically segments an image into areas of similar texture that correlate with different rock types. BorTex™ can further identify “spots” and “patches” from images for quantification of vugs and connectivity in carbonates. PoroSpect™ on the other hand transforms an FMI™ conductivity image to a porosity image (see below), then affords the opportunity to analyze the porosity distributions in a statistical sense. Finally, BorDip™ analyzes discontinuities in the images to automatically identify stratigraphic and structural dips, and fractures.
A limitation of these approaches to automated heterogeneity analysis from borehole image interpretation is that they involve treating the borehole image as a two-dimensional image to which image processing techniques are applied.
While there is a long history of academic and industrial approaches to the automated interpretation and modeling of borehole imagery (e.g. BorTeX™), there is limited academic or applied work on the application of geostatistical techniques for this purpose.
The recognition that borehole images can be mapped to petrophysical properties is well understood (see Delhomme et al., “Permeability and Porosity Upscaling in the Near-Wellbore Domain: The Contribution of Borehole Electrical Images”, (1996) SPE 36822 and Newberry et al., “Analysis of Carbonate Dual Porosity Systems from Borehole Electrical Images”, (1996) SPE 35158, incorporated by reference herein in their entireties).
Perhaps the best established transformation is that from resistivity to porosity space using the classic Archie saturation equation (see Fanchi et al., “Shared Earth Modeling” (2002) Elsevier, page 306, incorporated by reference herein in its entirety):
                              S          w          n                =                              aR            mf                                              Φ              m                        ⁢                          R              xo                                                          (        1        )            where Sw is the saturation of the wetting phase (0.00–1.00), n is the saturation exponent, α depends on the tortuosity (0.35–4.78), Rmf is the resistivity of the mud filtrate, Φ is the porosity (0.00–1.00), m is the cementation exponent (1.14–2.52), and Rxo is the resistivity of the flushed zone.
This relationship can be rearranged as follows:
                    Φ        =                              (                                          aR                mf                                                              S                  w                  n                                ⁢                                  R                  xo                                                      )                                1            m                                              (        2        )            
The PoroSpect™ application transforms the resistivity image data into porosity (Φ) using Equation (2) where the remaining Archie's parameters are either input by the user or derived from other logs. A 1.2-inch vertical window is then applied to these data to generate and analyze a porosity distribution histogram for every depth (0.1 inch vertical spacing) (see Newberry et al., “Analysis of Carbonate Dual Porosity Systems from Borehole Electrical Images”, (1996) SPE 35158). This technique has proven very powerful in identifying some aspects of porosity distribution such as dual-porosity. Note however, this technique effectively collapses the image data into a histogram, discarding spatial information (other than depth). It does not consider the three-dimensional geometry of the FMI™ sensors in the borehole.
An approach to analyze the geostatistical variation of porosity as seen in FMS borehole imagery has been suggested previously (see Delhomme et al., “Permeability and Porosity Upscaling in the Near-Wellbore Domain: The Contribution of Borehole Electrical Images”, (1996) SPE 36822). It is suggested that the geostatistics on a single pad can be analyzed for fine scale heterogeneity, and intermediate scale heterogeneity can be modeled across pads.
One object of the present invention is to provide a method to model formation heterogeneity in terms of geological or petrophysical properties.